Incentives?

Incentives?

Market PowerThe simplest departure from the price-taking equilibrium model is when

agents (firms) stop treating price as out of their control: they have marketpower, and the price or quantity they pick will their profits. Why does marketpower occur?

• Legal, technological, or resource barriers to entry

• Decreasing average total costs or subadditive costs (natural monopoly)

(which is Google?)

The Monopolist: Linear demandWe’ll work with a simple version of the quasilinear representative consumer

model, where

u(q,m) = aq − b

2q2 +m,

and the budget constraint is pq +m = w. Then the consumer’s problem is

maxqaq − b

2q2 − pq + w,

which gives the linear demand curve

p(q) = a− bq,

which we’ll stick with for this section.

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The Monopolist: Linear demandWhat would happen in the price-taking equilibrium? Set price equal to

marginal cost, so thata− bq = c,

and

q =a− cb

.

The Monopolist: Linear demandThe monopolist’s problem, then, is

maxqp(q)q − C(q)− F

where C(q) are variable costs and F is the fixed or sunk cost. With linearvariable costs,

maxq

(a− bq)q − cq − F

So the FONC isa− bq − bq − c = 0,

and the profit-maximizing quantity is

q∗ =a− c

2b,

exactly half the efficient quantity.

The Monopolist: General ruleWhat is the monopolist doing, in general? The FONC for

maxqp(q)q − C(q)− F

isp(q)− c′(q)︸ ︷︷ ︸

Marginal profit from marginal sale

+ p′(q)q︸ ︷︷ ︸Change in revenue × current sales

= 0.

The Monopolist: Lerner indexTo get more economic intuition on the magnitude of the problem, we’ll con-

vert the first-order condition into a Lerner index :

p(q)− c′(q)p(q)︸ ︷︷ ︸

Lerner index

= −dp(q)dq

q

p(q)= − 1

εd(q),

where εdq is the price elasticity of demand. The Lerner index then says thatthe fraction of the price that is attributable to market power — p(q) − c′(q)

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— is proportional to the inverse of the price elasticity of the demand curve.Smaller — less — elastic goods will have larger margins, higher profits, andmore inefficiency.

• Monopolists facing more inelastic demand make more money, and thelosses to society are greater.

Regulatory Solution: Ramsey Pricing

• Why not regulate the price, making it equal to marginal cost?

• (1) The monopolist usually has fixed costs, F , so that imposing of marginalcost pricing would lead to losses, and (2) marginal cost is not observable

• −→ impose a zero profit condition — like in a price-taking equilibrium —so the monopolist can recover his fixed costs

Then the monopolist solves

maxqp(q)q − c(q)− F

subject to p(q)q − c(q) = F .

Traditional Solution: Ramsey PricingThis gives a Lagrangian

L = p(q)q − c(q)− λ(p(q)q − c(q)− F ),

with FONC’s

(1− λ∗)(p′(q∗)q∗ + p(q∗)− c′(q∗)) = 0

−(p(q∗)q∗ − c(q∗))− F = 0.

The first equation is the standard monopoly FONC, saying that the Lernerindex should be -1/elasticity of demand

p(q∗)− c′(q∗)p(q∗)

=−1

εd(q∗)

and the second equation says that average cost pricing is Ramsey-optimal:

p(q∗) =c(q∗) + F

q∗.

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Regulatory Solution: Ramsey PricingIn the p(q) = a− bq, and c(q) = cq example,

pRamsey =c(q) + F

q= c+

F

q,

so the answer is to set the price equal to the firm’s marginal cost plus the averagefixed cost; this spreads fixed costs out over all the sales it makes.

Note that letting the firm freely maximize and then taxing its profits doesn’twork.

Regulatory Solution: Ramsey PricingHow does Ramsey/average cost pricing compare to price-taking equilibrium?

• If the cost function is linear and there are no fixed costs, C(q) = cq, sothat

p(q∗) =cq∗

q∗= c,

and Ramsey pricing is efficient.

• If the cost function is linear and there are fixed costs, C(q) = cq + F , sothat

p(q∗) =cq∗ + F

q∗= c+

F

q∗,

and Ramsey pricing will be nearly efficient as long as enough quantity isproduced relative to fixed costs (eg, a natural monopoly).

Regulatory solution: Ramsey pricingPros:

• Average total cost is observable, unlike marginal cost, so this is possible inpractice (public utilities, drugs, and other industries have been regulatedthis way; transfer pricing within firms (PwC))

• If costs are close to linear, Ramsey pricing is (almost) optimal

Cons:

• No reason to think costs are almost linear, so losses might still be large

• While ATC is observable, it might be complicated or costly for a regulatorto measure them

• In practice, the regulator has to set the price schedule before the monop-olist decides what to do: this requires knowing the demand curve and thefirm’s cost curve, which might be difficult to measure or forecast

• Economic profits are not always bad: innovation and investment oftencome from profits

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Regulatory Solution: break up the monopolistYou could call this the “nuclear option”.

• In the early 1980’s, the Bell telephone system/AT&T was broken up intoone long-distance carrier along with Bell labs, and seven regional compa-nies that were independently owned.

• “To break up a very tight network is something quite unprecedented,”said Alfred D. Chandler Jr., professor of business history at the HarvardBusiness School. “It was one of the best managed companies in the worldfor a long time. You go overseas and people there can’t understand whywe’re breaking up A.T.&T.”

• “We’ll get new technologies rushing forward,” said Ithiel de Sola Pool,director of the research program on communications policy at the Mas-sachusetts Institute of Technology.

• “It is the dumbest thing that has ever been done,” said Charles Wohlstet-ter, chairman of Continental Telecom Inc., an independent telephone com-pany. “You don’t have to break up the only functioning organization inthe country to spur innovation.”

Regulatory Solution: break up the monopolist

• “This article presents a new test for subadditivity of the cost function ...Applying ths test to the Bell System using 1947-77 time-series data, wereject the hypothesis that the Bell System’s cost function is subadditive atthe output levels produced between 1958-77. We find limited evidence thatthe Bell System did not optimally decentralize itself during these years andwas therefore operating inefficiently.” – A Test for Subadditivity of theCost Function with an Application to the Bell System, David S. Evans;James J. Heckman. The American Economic Review, Vol. 74, No. 4.(Sep., 1984), pp. 615-623.

• Subadditive means C(q + q′) ≤ C(q) + C(q′), so that there are scale eco-nomics: rejecting his hypothesis means that Bell was not really a naturalmonopoly, and breaking it up was potentially a good idea.

Regulatory Solution: break up the monopolistOften, regulators are unwilling to do something this drastic:

• Federal Baseball Club of Baltimore, Inc. v. National League of ProfessionalBaseball Players: comes down to interstate commerce clause — “The players, itis true, travel from place to place in interstate commerce, but they are not thegame. Not until they come into contact with their opponents on the baseballfield and the contest opens does the game come into existence. It is local in itsbeginning and in its end. Nothing is transferred in the process to those whopatronize it.” — Supreme Court decision

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• USFL v. NFL: “The United States Football League suffered what both sidesconsidered a resounding defeat in United States District Court in Manhattanyesterday when a jury found that the National Football League had violatedantitrust law but awarded the U.S.F.L. only $1 in damages... Although thejury found that the N.F.L. violated Section 2 of the Sherman Antitrust Actby having and ’willfully acquiring or maintaining a monopoly,’ in that it couldcontrol prices or exclude competition” — NYT article

Oligopoly

• Most industries are actually not monopolies or perfectly competitive, butsomewhere in the middle: firms have price power, but don’t control thewhole market

• Why do oligopolies arise?

– Standard barriers to entry

– Product differentiation

• The relevant policy concerns are usually about mergers and collusion

OligopolyWhat happens when there are N > 1 firms instead of just one, where each

knows it has market power?

• We imagine each firm takes the quantity choices of its opponents as fixedand selects its own quantity to maximize its profits

• We then find the quantity choices for all the firms at which each firm’sforecasts about its opponents are correct

This is called a Cournot Equilibrium or a Nash equilibrium: it’s just like a price-taking equilibrium, except that what you take as given — instead of the price— are the choices of your opponents.

OligopolySuppose all the firms are the same, so firm i of N ’s costs are just C(qi) = cqi.

Then a typical firm i faces the problem

maxqi

(a− b(q1 + q2 + ...+ qi + ...+ qN )) qi − cqi

Firm i takes the quantities of the other firms as given, and chooses his quantityto maximize the above profit function, giving the FONCa− N∑

j=1

qj

− bqi − c = 0.

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Now, since the firms are all the same, we’ll look for a solution where they all dothe same thing: qi = q∗ for all i, so that

(a−Nq∗)− bq∗ − c = 0.

OligopolyThis gives

q∗ =1

N + 1

a− cb

,

which is between the monopoly ((a − c)/2b) and perfectly competitive (a − c)quantities. The total quantity produced in the market is Nq∗, or

Q∗ =N

N + 1

a− cb

and the price is

p∗ = a− N

N + 1(a− c) = a

1

N + 1+

N

N + 1c.

Notice, as N gets large, p∗ gets closer and closer to c: the perfectly competitiveoutcome.

Oligopoly: Convergence to perfect competitionIf the price for N firms is

p∗N = a1

N + 1+

N

N + 1c,

consider the quantity p∗N − c, which is

p∗N − c =1

N + 1(a− c) ≈ a constant

N.

So the oligopoly price converges to the competitive price (c) at a rate of 1/N :this is really fast. At 10 equally competitive firms, you’re about 1/10-th thedistance from the competitive price; at 100, you’re about 1/100 the distance.

• In the presence of competition, oligopoly prices converge to competitiveones at a speed of O(1/N), so the best regulatory policy is usually toencourage competition.

Experimental evidence

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21000

24000

27000

30000

33000

10 15 20Number Invited

CFA

Average price by number invited

Oligopoly: Merger analysis and the HHIBut firms don’t want entry: they want to merge. Why?

• Economize on fixed costs (welfare-enhancing)

• Increase market power by pooling patents/resources (welfare-reducing)

• Increase market power by reducing competition (welfare-reducing)

The Herfindahl-Hirschman Index is intended to be a measure of industrial con-centration, defined as

HHI =

N∑i=1

s2i

where si is i’s share of total industry production, qi/Q. If all the firms havea small market share, they presumably have little market power, and HHI iscloser to zero. If a single firm does the vast majority of the production, thenHHI is closer to one. So this gives a zero-to-one-measure of the competitivenessof an industry.

Oligopoly: Merger analysis and the HHIThe Department of Justice actually uses the HHI to decide whether a pro-

posed merger presents a threat to competition. The Horizontal Merger Guide-lines state:

• An H below 0.01 indicates a highly competitive industry

• An H below 0.15 indicates an unconcentrated industry

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• An H between 0.15 to 0.25 indicates moderate concentration

• An H above 0.25 indicates high concentration

If the industry is moderately or highly concentrated, or if a merger would leadto a large increase in the HHI, the DOJ will typically investigate or challengethe merger.

Oligopoly: Merger analysis and the HHIFor our simple model, each firm produces q∗ = (a − c)/(b(N + 1)), so si =

1/N . Then we have

HHI =

N∑i=1

(1

N

)2

=1

N,

Then the guidelines say:

• An H with 100 or more firms indicates a highly competitive industry

• An H with more than 7 firms indicates an unconcentrated industry

• An H between 4 to 7 firms indicates moderate concentration

• An H with fewer than 4 firms indicates high concentration

Oligopoly: Merger analysis and Market DefinitionHere is a case that makes the issue of market definition clearer:

• In 2007, the FTC challenged a merger between Whole Foods and WildOats, arguing that they were “premium natural and organic supermar-kets”, distinct from conventional supermarkets. Apart from Whole Foodsand Wild Oats, the only other PNOS identified by the FTC were EarthFare in southeastern states and New Seasons in Oregon.

• Whole Foods/Wild Oats argued that they were basically a really nicesupermarket

• The Whole Foods CEO hadn’t helped when he previously said, “Safewayand other conventional retailers . . . cant really effectively focus onWhole Foods Core Customers without abandoning 90 percent of theirown customers”

• The merger was ultimately allowed, since the case was nutty

Merger analysis and Market DefinitionAn important feature of the case was:

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• “Based largely on testimony and studies from the defendants experts, thecourt found that conventional stores such as Safeway, Delhaize America,Krogers, and others had repositioned themselves to offer more naturaland organic products and would operate to constrain Whole Foods in thepost-merger market. It found that grocery shoppers are price sensitiveand frequently engage in cross-shopping, i.e., buying various grocery itemsfrom different stores in their local areas, and purchasing many, if not themajority, of their items at conventional stores.” — ABA analysis of ruling

Things went differently in FTC v Staples, when Staples tried to acquire OfficeDept in the late 1990’s:

• The court ruled that “office superstores” were a distinct market

• The merger was blocked, since it would have reduced the market to threefirms and considerably increased concentration

Oligopoly: Merger analysis and the HHIPros:

• The HHI is intuitive: larger market shares usually means more marketpower

• Gathering and computing market share data is easy

• The guidelines seem reasonable

Cons:

• The entire economic analysis will hinge on market definition, and this hashad lasting implications

• The HHI somewhat arbitrary: it’s not really tied to consumer welfare inany way

• Market power might not necessarily be driven by market share, or smallproduces might be taking the most advantage of their consumers

CollusionCollusion is when firms coordinate to act like a monopolist. There are two

flavors:

• Explicit collusion – firms get together and decide how to manipulate pricesand the penalty for deviating

• Tacit collusion – without saying so, firms settle into an unspoken agree-ment to manipulate prices

For the economist, both are the same thing, pretty much: illegal contracts arenot enforceable in court, so whether or not it’s tacit or explicit, the agreementmust be enforced by the threat of punishment from within the cartel. (Theyare not the same for lawyers)

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Collusion: mechanicsTo keep things simple, suppose there’s two firms, and they can charge a high

price or low price.

• If they both charge high prices, they split the monopoly profit, πmonopoly/2

• If they both charge low prices, they each get profits of zero

• If one charges a high price and the other charges the low price, the onecharging the low price gets πundercut > πmonopoly/2 and the one chargingthe high price gets zero

The interest rate is 0 < r < 1, so the firms discount future payoffs at a rate of

δ =1

1 + r.

For such a firm, the value of an asset that pays out one dollar a day forever is

1 + δ + δ2 + δ3 + ... =1

1− δ.

Collusion: mechanicsNow, one firm says to the other (over a call on throwaway cellphones or

through an interview in the WSJ)

• We are killing each other charging competitive prices

• I am going to raise my price, because reasons

• If you follow me and we raise our prices together, I will continue to main-tain a high price

• If you charge a low price ever again, I will go back to charging low prices

See how — if the other firm agrees this is in its best interests to follow — thisrequires no courts, no explicit agreements, nothing?

Collusion: mechanicsDoes the other firm agree to the collusive agreement?

• If it refuses, its payoff is

πu + δ0 + δ20 + ... = πu

• If it agrees, its payoff is

πmonopoly

2+ δ

πmonopoly

2+ δ2πmonopoly

2+ ... =

πmonopoly

2

1

1− δ

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• So agreeing is profitable if

πmonopoly

2

1

1− δ≥ πundercut,

or

δ ≥ πundercut − πmonopoly/2

πundercut.

So if firms are sufficiently patient — the interest rate (price of futureconsumption) is low enough — then collusion can be profitable, whethertactic or explicit.

Collusion: Policy responsesOptions:

• Courts and anti-trust suits: requires detection and evidence

• Subsidize entry into the market: potentially expensive

• Regulate the market

• Entrepreneurs as intermediaries

Market collusion: Porter (1983)

• Usually, cartels can’t observe opponents cheating on the agreement di-rectly: market prices are noisy

• “Secret price cutting” is then discouraged by punishing everyone, leadingto price wars

• “The JEC was a cartel which controlled eastbound freight shipments fromChicago to the Atlantic seaboard in the 1880s. It was formed in April1879 by an agreement of the railroads involved in the market. The firmsinvolved publicly acknowledged this agreement, as it preceded the passageof the Sherman Act (1890) and the formation of the Interstate CommerceCommission (1887). A separate agreement was reached for westboundshipments on the same railroad lines, primarily because of the essentialphysical differences of the products being transported.”

• “According to Ulen, there were several instances in which the cartel thoughtthat cheating had occured, cut prices for a time, and then returned to thecollusive price.”

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Market collusion: Porter (1983)

• Estimate price and quantity as

log(Qt) = α0 + α1 log(pt) + α2Lt + ε1t

log(pt) = β0 + β1 log(Qt) + β2St + β3It + ε2t

where Lt = 1 if the Great Lakes are open to navigation, It = 1 if apunishment is occurring, and St are industry “controls”.

• The idea is to use variation in Lt and St across time to guess at whetherpunishments are occurring: controlling for the lakes and industry char-acteristics, on average, prices should be similar, so unexplained drops indemand are due to the price war, It

Market collusion: Porter (1983)

Market collusion: Porter (1983)

• “The econometric results indicating that these episodes were concentratedin 1881, 1884, and 1885 are in keeping with the behavior of the JEC thatwas reported at that time.”

• Why did the wars occur? “Traditionally, breakdowns in cartel disciplinehave been attributed to demand slumps.” First, Porter finds that pricesare low and quantities are high preceding a price war, ceteris paribus.Second, the number of price war periods increased as the number of firmsincreased.

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Collusion in the LIBOR: Youle (2014)

• Trader: [Would] be nice if you could put 0.90% for 1mth cheers.

• Quote Submitter: Sure no prob. I’ll probably get a few phone calls butno worries mate!

• Trader: If you may get a few phone calls then put 0.88% then.

• Quote Submitter: Don’t worry mate – there’s bigger crooks in the marketthan us guys!

Rabobank, internal discussion

Collusion in the LIBOR: Youle (2014)

• 16 large banks are asked, “At what rate could you borrow funds, were youto do so by asking for and then accepting interbank offers in a reasonablemarket size just prior to eleven a.m. London time?”, the largest andsmallest four are discarded, and the average is computed. That’s theLIBOR.

• “While an enormous number of contracts reference the Libor, the Londoninterbank market, for which the Libor is supposed to represent the averageprice of funds, is small. This market was large in the 1980s, but has beenlargely been replaced by overnight and collateralized forms of lending.Repurchase agreements, commercial paper, overnight federal funds, andother close money market substitutes are now the primary vehicles throughwhich banks and other financial institutions exchange funds. This hasmade it increasingly difficult to verify submitted Libor quotes to actualinterbank trades as such trades are increasingly uncommon.”

Collusion in the LIBOR: Youle (2014)

• Let qt be the 16 firm’s quotes, and xt be bank characteristics.

• The Libor is

L(qt) =1

8

16∑i=1

I{qit ∈ IQR(qt)}qit,

the mean of the interquartile range of quotes

• Firms pick quotes qit to maximize

vi(xit)L(qt)︸ ︷︷ ︸Portfolio exposure

− δ(qit − βixit − εit)2︸ ︷︷ ︸Market reputation cost

+ ψiqit︸︷︷︸Regulatory reputation cost

• FONC:

qit =vi(xit)

2δ

partial

∂qitLi(qit) +

ψi

2δ+ xitβ + εit

• Use previous quotes from opponent banks as “instrumental variables”

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Collusion in the LIBOR: Youle (2014)

• “Hundreds of trillions of dollars worth of financial contracts were manip-ulated by large banks, who have since been fined billions of dollars byregulators from four countries.”

• “I find ... that changing the current mechanism for calculating the Liborcan make it considerably less vulnerable to manipulation. In particular,changing the Libor to use the median quote removes virtually all of itssystematic downwards bias in the sample period I examine.”

• “I find that the Libor was largely accurate prior to the financial crisisstarting in late 2007, but was since distorted downwards by eight basispoints.”

• “I calculate that U.S municipalities, which held $500 billion worth of in-terest rate swaps in 2010, would have lost $455 million from this eightbasis point shift over my sample period.”

• Despite the recent manipulation, the Libor is still widely used, and willremain largely unchanged in the medium term.”

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